Shin Jaehee, Ha Donghoon, Kwon Younghun
Department of Applied Physics, Center for Bionano Intelligence Education and Research, Hanyang University (ERICA), Ansan 15588, Korea.
Department of Applied Mathematics and Institute of Natural Sciences, Kyung Hee University, Yongin 17104, Korea.
Entropy (Basel). 2021 Nov 26;23(12):1583. doi: 10.3390/e23121583.
Recently, Schmid and Spekkens studied the quantum contextuality in terms of state discrimination. By dealing with the minimum error discrimination of two quantum states with identical prior probabilities, they reported that quantum contextual advantage exists. Meanwhile, if one notes a striking observation that the selection of prior probability can affect the quantum properties of the system, it is necessary to verify whether the quantum contextual advantage depends on the prior probabilities of the given states. In this paper, we consider the minimum error discrimination of two states with arbitrary prior probabilities, in which both states are pure or mixed. We show that the quantum contextual advantage in state discrimination may depend on the prior probabilities of the given states. In particular, even though the quantum contextual advantage always exists in the state discrimination of two nonorthogonal pure states with nonzero prior probabilities, the quantum contextual advantage depends on prior probabilities in the state discrimination of two mixed states.
最近，施密德和斯佩肯斯从态判别方面研究了量子上下文相关性。通过处理两个具有相同先验概率的量子态的最小错误判别，他们报告称存在量子上下文优势。同时，如果注意到一个引人注目的观察结果，即先验概率的选择会影响系统的量子性质，那么就有必要验证量子上下文优势是否取决于给定态的先验概率。在本文中，我们考虑两个具有任意先验概率的态的最小错误判别，其中这两个态可以是纯态或混合态。我们表明，态判别中的量子上下文优势可能取决于给定态的先验概率。特别地，尽管在两个具有非零先验概率的非正交纯态的态判别中量子上下文优势总是存在，但在两个混合态的态判别中量子上下文优势取决于先验概率。
